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01 Jul 2009, 07:02
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How many integers less than 10,000 are there in which sum of digits equals 5?
(A) 31
(B) 51
(C) 56
(D) 62
(E) 93
(A) 31
(B) 51
(C) 56
(D) 62
(E) 93
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01 Jul 2009, 08:09
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And should be C - 56
The possible combinations are
2,3;...... 4,1;...... 5;....... 1,1,3;...... 2,2,1;...... 1,1,1,2
permutations are as follows (using 4 places, and putting zeros in front for 1,2 and 3 digit numbers)
0,0,2,3 = !4/!2 = 12
0,0,4,1 = 12 (same as above)
0,0,0,5 = !4/!3 = 4
0,1,1,3 = !4/!2 = 12
0,2,2,1 = !4/!2 = 12
1,1,1,2 = !4/!3 = 4
Total = 12*4 + 4*2 = 56
Hope the explanation is clear.
btw, thanks for the great question.
The possible combinations are
2,3;...... 4,1;...... 5;....... 1,1,3;...... 2,2,1;...... 1,1,1,2
permutations are as follows (using 4 places, and putting zeros in front for 1,2 and 3 digit numbers)
0,0,2,3 = !4/!2 = 12
0,0,4,1 = 12 (same as above)
0,0,0,5 = !4/!3 = 4
0,1,1,3 = !4/!2 = 12
0,2,2,1 = !4/!2 = 12
1,1,1,2 = !4/!3 = 4
Total = 12*4 + 4*2 = 56
Hope the explanation is clear.
btw, thanks for the great question.
Hussain15
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GMAT 1: 680 Q48 V34
Schools: Stanford '14 (D) Booth '14 (D) Johnson '14 (D)
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01 Jul 2009, 09:37
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I wonder if I could have understood this!! .
Perhaps I need to have initial study on this, then I can take it more easily!!
Thanks for the solution though!!
Posted from my mobile device
.Perhaps I need to have initial study on this, then I can take it more easily!!
Thanks for the solution though!!
Posted from my mobile device
